Pricing Errors Research Articles

Learning for infinitely divisible GARCH models in option pricing

Abstract This paper studies the option valuation problem of non-Gaussian and asymmetric GARCH models from a state-space structure perspective. Assuming innovations following an infinitely divisible distribution, we apply different estimation methods including filtering and learning approaches. We then investigate the performance in pricing S&P 500 index short-term options after obtaining a proper change of measure. We find that the sequential Bayesian learning approach (SBLA) significantly and robustly decreases the option pricing errors. Our theoretical and empirical findings also suggest that, when stock returns are non-Gaussian distributed, their innovations under the risk-neutral measure may present more non-normality, exhibit higher volatility, and have a stronger leverage effect than under the physical measure.

Autoencoder asset pricing models

We propose a new latent factor conditional asset pricing model. Like Kelly, Pruitt, and Su (KPS, 2019), our model allows for latent factors and factor exposures that depend on covariates such as asset characteristics. But, unlike the linearity assumption of KPS, we model factor exposures as a flexible nonlinear function of covariates. Our model retrofits the workhorse unsupervised dimension reduction device from the machine learning literature – autoencoder neural networks – to incorporate information from covariates along with returns themselves. This delivers estimates of nonlinear conditional exposures and the associated latent factors. Furthermore, our machine learning framework imposes the economic restriction of no-arbitrage. Our autoencoder asset pricing model delivers out-of-sample pricing errors that are far smaller (and generally insignificant) compared to other leading factor models.

Investor sentiments and pricing errors

PurposeThis paper computes the pricing errors of S&P 500 index by employing the valuation model developed by Doran et al. (2009) and investigates its response to individual and institutional investor sentiments. This study contributes to the literature by looking at both rational and quasi-rational sentiments and how noise trading and investments based on fundamentals affect pricing errors.Design/methodology/approachThis paper computes the pricing errors of S&P 500 index by employing the valuation model developed by Doran et al. (2009) and investigates its response to individual and institutional investor sentiments.FindingsResults show that pricing errors are persistent and stock prices systematically deviate from their intrinsic values. The authors also find that both individuals and institutional investors form their expectations based on risk factors as well as noise; however, institutional investors seems to be more driven by rational factors. The findings also suggest that institutional investors have a significant power to cause pricing errors due to unpredictable changes in their sentiments while small investors lack such ability to move stock prices away from their intrinsic values. Additionally, this paper finds that quasi-rational (rational) investor sentiments have positive (negative) impact on pricing errors suggesting that trading based on noise is an important determinant of pricing errors while investors' expectations stemming from fundamentals play an important role in improving market efficiency.Research limitations/implicationsThe impact of rational outlook due to changes in fundamentals seems to be greater than that of noise on the pricing errors, consistent with both risk-based and behavioral models of the asset pricing literature.Originality/valueOur study contributes to the existing literature in the following ways: first, the authors employ most recent data to compute mispricing for the market index and investigate if it is persistent and systematic. Second, the authors decompose sentiment variables into rational and quasi-rational components and trace their dynamics to better understand the role of risk factors and noise in the formation of sentiments. Third, the authors investigate the relative impact of individual and institutional investor sentiments on mispricing. Lastly, the authors examine the response of pricing errors to both rational and quasi-rational sentiments of individual and institutional investors.

Inference for variance risk premium

PurposeWith the presence of pricing errors, the authors consider statistical inference on the variance risk premium (VRP) and the associated implied variance, constructed from the option prices and the historic returns.Design/methodology/approachThe authors propose a nonparametric kernel smoothing approach that removes the adverse effects of pricing errors and leads to consistent estimation for both the implied variance and the VRP. The asymptotic distributions of the proposed VRP estimator are developed under three asymptotic regimes regarding the relative sample sizes between the option data and historic return data.FindingsThis study reveals that existing methods for estimating the implied variance are adversely affected by pricing errors in the option prices, which causes the estimators for VRP statistically inconsistent. By analyzing the S&P 500 option and return data, it demonstrates that, compared with other implied variance and VRP estimators, the proposed implied variance and VRP estimators are more significant variables in explaining variations in the excess S&P 500 returns, and the proposed VRP estimates have the smallest out-of-sample forecasting root mean squared error.Research limitations/implicationsThis study contributes to the estimation of the implied variance and the VRP and helps in the predictions of future realized variance and equity premium.Originality/valueThis study is the first to propose consistent estimations for the implied variance and the VRP with the presence of option pricing errors.

Arbitrage Pricing Model Based on Factor Analysis-Random Forest Regression and its application

Firstly, this paper establishes K-factor linear model and arbitrage pricing model (ATP) according to ‘the Asset Pricing Model-Arbitrage Pricing Theory’, Then from 2001 to 2017, the Statistical Yearbook of the National Bureau of Statistics collected 10 factors as the original factors such as gross national product, gross industrial product and gross tertiary industry product. After synthesis and simplification, three common factors are extracted to replace ten original factors.The first common factor variable is used to reflect the overall economic level of the country;The second common factor variable reflects a country's inflation rate;The third public factor variable reflects the total annual net export trade situation of the country. After the common factor is determined, the value of the common factor is calculated from the original data.Collect the annual return of 10 stocks for 17 years and do twice random forest regression,we get the arbitrage pricing model. Then, based on the same common factor data, another arbitrage pricing model is obtained by imitating the linear regression method of previous similar papers. By comparing the pricing error, we can find the pricing effect of the model obtained by random forest regression is better than that of the model obtained by linear regression.

A new measure of model misspecification with the no-arbitrage constraint: extending the second Hansen–Jagannathan distance

This paper proposes a new measure for evaluating asset pricing models with the no-arbitrage constraint which naturally extends the classical (second) distance of Hansen and Jagannathan (J Polit Econ 99(2):225–262, 1991, J Finance 52(2):57–590, 1997). The new measure is designed to capture model misspecifications in terms of arbitrary moments/co-moments in the stochastic discount factors in contrast to the classical Hansen–Jagannathan distance which only uses information contained in the first two moments/co-moments. The new measure $$D_{p}^{+}$$ is defined for any $$1<p<+\infty$$ , which reduces to the Hansen–Jagannathan distance when $$p=2;$$ but for other values of p, the new measure captures model misspecifications in terms of higher or lower moments/co-moments of the model stochastic discount factors and asset returns. An explicit representation of the new measure is obtained by solving the conjugate problem using convexity arguments. The relationship between the new distance and pricing errors is also established. An empirical analysis of the Fama–French 6-portfolios is conducted to illustrate the applications of the new measure.

Affine multivariate GARCH models

Abstract This paper introduces a class of Affine multivariate GARCH models. Our setting offers flexibility to accommodate stylized facts of asset returns like dynamic conditional correlation and a covariance dependent pricing kernel. The model admits a closed-form recursive representation for the moment generating function under both historical and risk-neutral measures, permitting efficient multi-asset option pricing and risk management calculations. We illustrate the applicability and impact of our framework on the five assets for which volatility indices are made publicly available, together with the S&P 500 Index. We demonstrate that our methodology is remarkably faster than Monte Carlo simulation when pricing two-assets options. We confirm the importance of incorporating a covariance-dependent pricing kernel compared to a linear pricing kernel by reporting large and economically significant changes in the price of two-asset options. Similarly, our single-factor Index model structure for the marginal can lead to differences of up to 70% in the price of single-asset options and empirical option pricing errors that are up to 41% smaller than what is obtained with a univariate model with a linear pricing kernel.

An Optimal Solution for Eco-reliability Stochastic Modeling of Simultaneous Reconfiguration of Distribution Networks and Allocation of Renewable Energy Resources, Capacitors and D-facts

Objective: A new method based on stochastic modeling of simultaneous optimal reconfiguration of distribution networks and allocation of multiple Distribution STATic COMpensator and renewable energy resources as new developed technologies is suggested in this paper. Background: This problem involves vital uncertain parameters such as: intermittent nature of renewable energy sources, load forecasting and market price errors. Krill Herd Algorithm as a powerful optimization solution is applied to solve suggested problem. Methods: Several effective cost based consequences can be achieved by proposed technique like: DG units installation and operation costs, D-Statcom installation cost, capacitor costs, cost of purchased energy from the transmission network, active and reactive power losses cost, line upgrade cost and distribution system reconfiguration cost. Results: In addition, energy not supplied as a vital reliability index incorporated in the cost function aims to improve network’s reliability efficiently. Conclusion: IEEE 33 bus radial distribution system is used here to check the practicability of the proposed scheme.

Is deflation costly after all? The perils of erroneous historical classifications

SummaryI estimate average economic activity during periods of inflation and deflation while accounting for measurement errors in 19th century prices. These measurement errors lead to underestimation (overestimation) of economic activity during periods of inflation (deflation). By exploiting multiple deflation indicators, it is possible to recover the true relationship; the shortfall of US industrial production growth during periods of deflation ranges from −4.5 pp to −7.6 pp, instead of −2 pp. I also find a negative relationship between deflation and real activity in the UK. I then examine the cross‐country variation in the estimates for eleven countries. The patterns are consistent with stronger biases for countries with more serious measurement errors in prices.

Algorithmic trading in turbulent markets

Does Algorithmic Trading (AT) exacerbate price swings in turbulent markets? We find that stocks with high AT experience less price drops (surges) on days when the market declines (increases) for more than 2%. This result is consistent with the view that AT minimizes price pressures and mitigates transitory pricing errors. Further analyses show that the net imbalances of AT liquidity demand and supply orders have smaller price impacts compared to non-AT net order imbalances and algorithmic traders reduce their price pressure by executing their trades based on the prevailing volume-weighted average prices.

Optimal convergence trading with unobservable pricing errors

We study a dynamic portfolio optimization problem related to convergence trading, which is an investment strategy that exploits temporary mispricing by simultaneously buying relatively underpriced assets and selling short relatively overpriced ones with the expectation that their prices converge in the future. We build on the model of Liu and Timmermann (Rev Financ Stud 26(4):1048–1086, 2013) and extend it by incorporating unobservable Markov-modulated pricing errors into the price dynamics of two co-integrated assets. We characterize the optimal portfolio strategies in full and partial information settings under the assumption of unrestricted and beta-neutral strategies. By using the innovations approach, we provide the filtering equation which is essential for solving the optimization problem under partial information. Finally, in order to illustrate the model capabilities, we provide an example with a two-state Markov chain.

An excellent approximation for the m out of n day provision

The m out of n day provision (MooN) of convertible bonds is difficult to handle. To approximating the MooN better, this paper proposes an approach named the conditional range probability (CRP). CRP is the simulated probability of the MooN being reached within a price range at a future time, conditional on today’s price of the underlying, and can be incorporated into any conventional derivatives pricing method. For a purposely designed exotic call option with a 20 out of 30 day provision, CRP under finite difference is found to outperform significantly several existing approaches and produce a mean pricing error of 1% over a wide range of initial underlying prices for the exotic call. The result implies that finite difference utilizing CRP will yield excellent approximating prices for convertible bonds.

Deep Learning in Asset Pricing

We use deep neural networks to estimate an asset pricing model for individual stock returns that takes advantage of the vast amount of conditioning information, while keeping a fully flexible form and accounting for time-variation. The key innovations are to use the fundamental no-arbitrage condition as criterion function, to construct the most informative test assets with an adversarial approach and to extract the states of the economy from many macroeconomic time series. Our asset pricing model outperforms out-of-sample all benchmark approaches in terms of Sharpe ratio, explained variation and pricing errors and identifies the key factors that drive asset prices.

Credit Spreads, Leverage and Volatility: a Cointegration Approach

This work documents the existence of a cointegration relationship between credit spreads, leverage and equity volatility for a large set of US companies. It is shown that accounting for the long-run equilibrium dynamic between these variables is essential to correctly explain credit spread changes. Using a novel structural model in which equity is modelled as a compound option on the firm's assets, a new methodology for estimating the unobservable market value of the firm's assets and volatility is developed. The proposed model allows to significantly reduce the pricing errors in predicting credit spreads when compared with several structural models. In terms of correlation analysis, it is shown that not accounting for the long-run equilibrium equation embedded in an Error Correction Mechanism (ECM) results into a misspesification problem when regressing a set of explanatory variables onto the spread changes. Once credit spreads, leverage and volatility are correctly modelled, thus allowing for a long-run equilibrium, the fit of the regressions sensibly increases if compared to the results of previous research. It is further shown that most of the cross-sectional variation of the spreads appears to be more driven by firm-specific characteristics rather than systematic factors.

Equity Financing Risk

A risk factor linked to aggregate equity issuance conditions explains the empirical performance of investment factors based on the asset growth anomaly of Cooper, Gulen, and Schill (2008). This new risk factor, dubbed equity financing risk (EFR) factor, subsumes investment factors in leading linear factor models. Most importantly, when substituted for investment factors, the EFR factor improves the overall pricing performance of linear factor models, delivering a significant reduction in absolute pricing errors and their associated t-statistics for several anomalies, including the ones related to R&amp;amp;D expenditures and cash-based operating profitability.

Data Envelopment Analysis and Multifactor Asset Pricing Models

Recent literature shows that market anomalies have significantly diminished, while research on market factors has largely improved the performance of asset pricing models. In this paper we study the extent to which data envelopment analysis (DEA) techniques can help improve the performance of multifactor models. Specifically, we test the explanatory power of the Fama and French three-factor model, combined with an additional factor based on DEA, on a sample of 2101 European equity funds, for the period from 2001 to 2016. Accordingly, we first form the fund portfolios that constitute our test assets and create the efficiency factor. Secondly, we estimate the prices of risk tied to the four factors using ordinary least squares (OLS) on a two-stage cross-sectional regression. Finally, we use the R-squared statistic estimated by generalized least squares (GLS), as well as the Gibbons Ross and Shanken test and the J-test for overidentifying restrictions in order to study the performance of the model, including and omitting the efficiency factor. The results show that the efficiency factor improves the performance of the model and reduces the pricing errors of the assets under consideration, which allows us to conclude that the efficiency index may be used as a factor in asset pricing models.

Multi-objective model for simultaneous distribution networks reconfiguration and allocation of D-STATCOM under uncertainties of RESs

This paper proposes an approach for simultaneous placement of distribution static compensator (D-STATCOM) and renewable energy sources (RESs) and distribution system reconfiguration (DSR) based on stochastic multi-objective modelling. Associated uncertainties of RESs in generating power, market price errors and load forecasting are modelled in this problem. The problem is optimised by non-dominated sorting genetic algorithms-II (NSGA-II) and then the best compromise solution is specified with fuzzy set theory. The aim of optimisation is to minimise installation and operation costs of distributed generation (DG) units, cost of D-STATCOM installation, the cost of procured energy from the transmission grid, costs of reactive and active power losses, line upgrade cost and DSR expense. A risk-based model of energy not supplied (ENS) as a reliability index is considered in the objective function to improve the reliability of the system. The proposed approach is validated on the IEEE 33-bus test grid.

Granular Uncertainty and Disastrous Misallocation

We develop an endogenous growth model with heterogeneous firms, intermediate goods, and financial frictions, in which misallocation emerges analytically as a crucial state variable. In equilibrium, misallocation endogenously generates long-run uncertainty about economic growth by distorting innovation decisions, leading to significant welfare losses and risk premia in capital markets. Empirically, we construct a misallocation measure motivated by our model. We find evidence for misallocation-driven low-frequency movements in both aggregate growth and stock returns. A two-factor model with market and misallocation factors prices size, book-to-market, momentum, and bond portfolios with an R-squared and a mean absolute pricing error close to the Fama-French three-factor model.

The Fama-French’s five-factor model relation with interest rates and macro variables

Innovations in variables describing future investment opportunities command a risk premium and are correlated with Fama-French factors. As showed in literature, shocks to the aggregate dividend yield and term spread, default spread, and one-month T-bill rate are proxies for HML and SMB factors. However, in the context of five-factor model, they cannot explain RMW. As CPI is related to operational profitability, and so does RMW, we include its unanticipated shocks in the set of macro variables and factors to help explaining the cross section of returns. In the presence of CPI, RMW loses its explanatory power, and, combined with term structure’s slope innovations, all Fama-French factors lose their explanatory ability and the pricing errors become statistically close to zero. We show that for US data, inflation’s innovations not only proxy for RMW, but a model including only excess market returns, shocks to CPI and term structure’s slope explain the cross section of average returns better than innovations to the previous literature’s four-variable set and Fama-French five-factor model.

Portfolio Liquidity: Is the Whole More Than the Sum of Its Parts?

Active ETFs are less liquid than their underlying portfolios. This finding, which contrasts with that for passive ETFs, is attributed to uncertainty of future holdings of active ETFs. In addition, while diversification generally reduces firm-specific information asymmetry and improves portfolio liquidity, the liquidity of active ETFs is adversely affected by diversification, consistent with the substitution effect between diversification and liquidity documented in the literature. Furthermore, we show the gap between active ETF and underlying liquidity varies cross-sectionally and over time and can be explained by differences in size and volume between ETFs and their underlying portfolio, ETF age, and ETF pricing errors.